Deliberate mistake: In the beginning of the movie, we see Marty play his black Ibanez during the band try-outs. Later, we see it on his bed when Doc calls him and when he wakes up the next day in this alternate timeline. We never see him bring it home after school or when he goes home at night before dinner.
Suggested correction: Maybe one of the band members brought it back to his house for him. Maybe he forgot it and picked it up again later, off camera. Maybe he has 2. Maybe the guitar he is using at the try-out isn't his. So many possibilities.
Factual error: When Marty hits his head on the DeLorean's steering wheel, the car's horn honks. This is inaccurate to the design of real-world DeLoreans, as a DMC-12's horn button is actually located at the end of the turn signal lever rather than in the steering wheel. (01:39:27)
Suggested correction: You can't see his left hand and he could have accidentally pushed it when he hit his head. Or Dr. Bown customized the steering wheel so the horn is in it, like he customized the entire interior of the car.
I thought the point was that the car was so unreliable that when hit his head on the steering wheel, the horn went on. Makes sense to me. I own a DeLorean by the way.
Revealing mistake: When Marty crosses the park in front of the court house and the camera pans around following Marty while showing the town, watch one of the buildings in the middle background. Part of the building is grey and has 2 windows and is supposed to have a slanted roof, but if you watch closely, it appears that building is in fact only a wall with nothing behind it. (00:34:40)
Suggested correction: Nothing really specifies that the building is only a wall. It definitely could be, but since there are no camera angles showing the back or sides of the building, it's not really fair to call this a mistake.
Continuity mistake: When Marty is riding his skateboard to school in the beginning, he waves to a driver and you can see his wearing a watch on his left hand. However, look at his left hand when he meets up with Jennifer, and you'll see that it's gone. (00:06:10 - 00:07:00)
Suggested correction: There's a time-lapse directly before Marty arrives at school. There was plenty of time for him to remove the watch offscreen.
Trivia: The town hall building is also seen in the Voyagers TV show.
Suggested correction: The Town Hall building is in over 100 movies and TV shows since it is a building in Courthouse Square at Universal Studios. It has also appeared in Gremlins, The Twilight Zone, To Kill a Mockingbird, Knight Rider, Leave It To Beaver, Parenthood, Saving Mr. Banks, and Psycho II, to name some of a few of the more commonly known. I don't think its common appearance makes this trivia relevant.
I'd say it makes it more relevant. Just add the multiple appearances of the building.
Other mistake: Just before Marty starts playing Johnny B Goode on stage, he tells the band members to watch for changes and other guidance advice to start the song. When the song starts, ALL the band members (who have never heard this song before) suddenly play all the chord changes perfectly and even the drums are perfect like the real song. In reality, never hearing that song before, the band would not have had this song perfected like that - every note and instrument sound.
Suggested correction: This is, of course, done intentionally to make the song sound like it actually is. It's highly unlikely but not impossible that these musicians put it all together just as the actual song sounds. You also have to keep in mind that the idea is given that Chuck Berry came up with the song hearing it through the telephone, so that's why the actual song sounds the same, as he is just mimicking what he heard.
Besides which, if this posting were valid, every movie musical in history would be riddled with similar errors.
Continuity mistake: As Doc turns the plutonium jar on the back of the DeLorean, the little thing sticking out of the jar slides greatly down, without any motion of moving. (00:27:15)
Suggested correction: Wrong. It does show motion as it slides down, it just moves very quickly.